Irrationality proof of certain Lambert series using little q-Jacobi polynomials

We apply the Pade technique to find rational approximations to h(+/-)(q(1), q(2)) = (k=1)Sigma(infinity) q(1)(k)/1 +/- q(2)(k), 0 < q(1), q(2) < 1, q(1) is an element of Q, q(2) = 1/p(2), p(2) is an element of N\ {1}. A separate section is dedicated to the special case q(i) = q(ri), r(i) is an element of N, q = 1/p, p is an element of N\ {1}. In this construction we make use of little q-Jacobi polynomials. Our rational approximations are good enough to prove the irrationality of h(+/-) (q(1), q(2)) and give an upper bound for the irrationality measure. (C) 2009 Elsevier B.V. All rights reserved.